Then, we say that an independent set in \(H\)  of size \(|V(G)|\)  is a DP-coloring of \(G\)  with respect to \(H\) . If \(G\)  always has a DP-coloring for every \(f\) -fold cover \(H\)  of \(G\) , then we say that \(G\)  is DP-\(f\) -colorable.
If \(f\)  is a constant function \(f(v) = k\) , then we say that \(H\)  is a \(k\) -fold cover of \(G\) , and if \(G\)  always has a DP-coloring for every \(k\) -fold cover \(H\)  of \(G\) , then we say that the DP-chromatic number of \(G\)  is at most \(k\) , and we write \(\chi _{DP}(G) \le k\) .
Given a cover \(H\)  of \(G\) , we often refer to the vertices of \(H\)  as colors, and if \(c \in L(v)\)  for a vertex \(v \in V(G)\) , then we say that the color \(c\)  is above \(v\) . Note that when \(f(v) = k\)  is a constant function, if the cliques in \(H\)  corresponding to vertices in \(G\)  are replaced with independent sets, and if each matching between sets \(L(u)\)  and \(L(v)\)  is a perfect matching, then \(H\)  is a \(k\) -sheeted covering space of \(G\) , and a DP-coloring of \(G\)  is equivalent to an independent transversal of the fibers in \(H\)  above the vertices of \(G\)  (see [1]} for an introduction to graphs as topological spaces).
